Replicated multi-channel sensors for decucing ink thicknesses in color printing devices

ABSTRACT

A method and computing system are proposed for deducing ink thickness variations from solid-state multi-sensor measurements performed online on a printing press or printer. The computed ink thickness variations enable controlling the ink deposition and therefore the color accuracy. Ink thickness variations are expressed as ink thickness variation factors incorporated into an ink thickness variation and sensor response enhanced spectral prediction model. The ink thickness variation computing system comprises multi-channel sensor devices (e.g. red, green, blue, near infra-red), a processing module, and a computing system. The multi-channel sensor devices are replicated over the width of the print sheet. Preferably embodied by Single Photon Avalanche Diodes (SPADs), due to their high-speed acquisition capabilities, they provide responses according to the reflectance of small area segments within a print sheet. The processing module accumulates the digital sensor responses and forwards them to the computing system, which deduces the ink thickness variations.

The present patent application is a continuation-in-part of U.S. patentapplication Ser. No. 10/631743, Prediction model for color separation,calibration and control of printers, inventors R. D. Hersch, P. Emmel,F. Collaud, filed Aug. 1, 2003.

BACKGROUND OF THE INVENTION

The present invention relates to the field of color printing and morespecifically to the control of color printer actuation parameters. Itdiscloses a new concept of non-expensive replicated illuminating andsensor devices placed on the printer in face of the moving paper sheetsas well as a spectral prediction model extension adapted to the proposedset of illuminating and sensor devices.

Color control in printing presses is desirable in order to ensure thateffectively printed colors correspond to the desired colors, i.e. thecolors expected by the prepress color separation stage. Colorconsistency is desirable both across consecutive sheets of a multi-sheetprint job and also from print job to print job.

In the prior art, densitometers were often used to control the amount ofink of single ink printed patches. The densitometer measures the opticaldensity, which is an approximate measure of the ink thickness. In theprior art, the control of print actuation parameters affecting theprinted output such as the ink thickness is generally performed by anoperator or by an apparatus measuring the density of solid ink or ofhalftone ink patches, see U.S. Pat. No. 4,852,485 (Method of operatingan autotypical color offset machine, Inventor F. Brunner, issued Aug. 1,1989). Special patches are usually integrated along the borders ofprinted sheets and serve as a means to measure their density. Thesespecial patches need however to be subsequently cut out.

U.S. Pat. No. 6,230,622 (Image data-oriented printing machine and methodof operating the same, to P. Dilling, issued May 15, 2001) teaches amethod for operating a printing machine with an expert system whichdetermines the effect of the interaction of a large number of printparameters and acts on some of these parameters in order to reach a highprint quality. The proposed method relies only on density measurements.Due to the large number of parameters which need to be taken intoaccount, this solution seems complex and costly.

U.S. Pat. No. 5,903,712, Ink separation device for printing press inkfeed control, to X. X. Wang, and R. J. Nemeth, filed Oct. 5, 1995,issued May 11, 1999, teaches an ink separation device or process wherered, green, blue and infra-red scalar reflection values within a printedsheet are measured and converted into cyan, magenta, and yellow dot sizevalues according to a previously initialized transfer function. Bycomparing the so-obtained dot size values with reference dot sizevalues, a dot size ratio is derived to adjust the ink feed rate of thepress. The transfer function is a multi-variable polynomial of order 6.It comprises about 80 different coefficients which need to be regressedfor each combination of paper and ink set. A specially printed test formwith hundreds of patches is needed to enable these regressions. In thatinvention, the relationship between 4 channel sensor responses and theink dot sizes is considered to be unknown, i.e. a black box whosebehavior is modeled by the multi-variable high-order polynomial. Suchhigh order polynomials are known to oscillate between the known valuesof input/output variables and therefore do not always provide a correctmapping between sensor input variables and ink dot size outputvariables. In contrast, in our invention, we rely on a physically-basedspectral prediction model describing the interaction of light, inkhalftones and paper, as well as the ink spreading phenomenon. The modelwe propose is therefore robust and each of its elements (paperreflectance, ink transmittances, effective surface coverages) isseparately characterized from spectral reflectance or from multi-channelsensor response measurements.

U.S. Pat. No. 6,684,780, Ink control in printing press, filed Jan. 212003, issued Feb. 3, 2004, to Y. Shiraishi, teaches a method for ink keyaperture control by using a color difference between an original imageand an RGB CCD camera image of the print. By using a conversion table,color differences are converted into corresponding desired densitycorrections, which, through a second conversion table, are convertedinto ink key aperture correction values. Since these two conversiontables are deduced from experiments which may have been performed underdifferent printing conditions (temperature, settings of the press,etc.), the control of the ink aperture is not precisely adapted to thecurrent operating conditions of the press. In addition, experience showsthat it is very difficult to control the ink feed of 4 inks (c,m,y,k)with a 3-sensor system only. Experience also shows that using a spectralprediction model incorporating explicitly the ink thickness termsprovides more robustness than a pure colorimetric approach.

U.S. Pat. No. 6,611,357, Method of stipulating values for use in thecontrol of a printing machine, to K. Wendt and P. Schramm, filed Jan.26, 2001, issued Aug. 26, 2003, teaches a method for controllingprinters by determining according to the surface coverages of individualinks within an original image element the predicted (desired) colorspectrum, and achieving that color spectrum by varying the actual areacoverages of the individual inks by multiplicative factors deduced fromspectra predictions. Spectra are predicted according to a weightedaverage of the reflection spectra of the inks, the weights beingdetermined by the respective surface coverages of the inks. Thereflectance spectra of ink superpositions are not considered. It isknown in the art that no accurate spectral or color predictions can bemade without considering explicitly the reflectance of superposed inks.

U.S. Pat. No. 6,679,169, Ink control model for controlling the ink feedin a machine which processes printing substrates, filed Oct. 24, 2002,issued Jan. 20, 2004, to Anweiler, Gateaud, Hauck and Mayer teaches amethod for controlling the ink feed in a printing press by deducing theink feed rate from stored physical properties of inks and paper. Thatmethod does not consider controlling the ink feed rate according tosensor responses of illuminated polychromatic halftones.

U.S. Pat. No. 4,975,852, Process and apparatus for the ink control of aprinting machine, to G. Keller and H. Kipphan, filed Jan. 5, 1989,issued Dec. 4, 1990, U.S. Pat. No. 5,182,721, Process and apparatus forcontrolling the inking process in a printing machine, to H. Kipphan, G.Loffler, G. Keller and H. Ott, filed Sep. 28, 1990, issued Jan. 26,1993, and U.S. Pat. No. 6,041,708, Process and apparatus for controllingthe inking process in a printing machine, to H. Kipphan, G. Loffler, G.Keller and H. Ott, filed Aug. 22, 1994, issued Mar. 28, 2000 teachmethods to derive ink layer thickness variations from spectralreflectance differences of specially printed test patches by convertingthese differences to CIELAB differences and by multiplying thesedifferences by the inverse of a matrix whose components are derivativesof the CIELAB components in respect to the cyan, magenta and yellow inkthicknesses. The elements of the matrix are dependent on the areacoverage of the inks and need therefore to be calibrated for eachconsidered test patch.

U.S. Pat. No. 6,564,714, Spectral color control method, to D. Brydgesand E. Tobiason, Jul. 26, 2001, issued May 20, 2003, teaches a method toderive ink layer thickness correction values from spectral reflectancedifferences of specially printed test patches. Ink layer thicknessdifferences are obtained by multiplying the spectral reflectancedifference vector with a correction matrix expressing the derivatives ofthe ink layer thicknesses in respect to each of the monochromaticreflectance values. The elements of the correction matrix are dependenton the area coverage of the inks and need therefore be calibrated foreach test patch. In contrast, our invention provides a singlecomputation model for deriving ink thickness variations from halftoneprints. It does not require halftone area coverage dependentcalibrations to be performed.

U.S. Pat. No. 7,077,064, Methods for measurement and control of inkconcentration and film thickness, to D. Rich, filed Apr. 19, 2005,issued Jul. 18, 2006, teaches a method to deduce ink thickness as wellas ink concentration from red, green and blue responses of a camera,using a variant of the Kubelka-Munk model. It is known that theKubelka-Munk model only works on uniformly diffuse layers and istherefore not applicable to halftones. In contrast, our inventiondeduces ink thickness variations from halftones.

US parent patent application Ser. No. 10/631743 (Prediction model forcolor separation, calibration and control of printers, inventors R. D.Hersch, P. Emmel, F. Collaud, filed Aug. 1, 2003) teaches a method todeduce the ink thicknesses for a color patch printed with 2, 3 or 4inks. The method works for deducing the ink thicknesses on single inkpatches, on two ink patches and on 3 ink patches. But due to theuncertainty between joint variations in the ink thicknesses of cyan,magenta, and yellow and a variation in thickness of black, the methoddoes not work well for the set of cyan, magenta, yellow and black inks.In addition, that method does not teach how to calibrate the predictionmodel with halftones that are an integral part of a printed documentpage delivered to a customer. The present invention improves upon thatapplication by introducing a 4^(th) infra-red sensor to separate inkthickness variations of black from joint ink thickness variations ofcyan, magenta and yellow. In addition, the present invention clearlyseparates the calibration process into an offline calibration withspectral measurement devices on specially printed patches and an onlinecalibration with multi-sensor responses on halftones located within anormal printed page.

U.S. patent application Ser. No. 10/698667 (Inks Thickness Consistencyin Digital Printing Presses, to Staelin et al., filed Oct. 31, 2003)teaches a model for estimating ink thickness control parameters such asthe developer voltage in case of an electrographic printer. This modeltakes as input values measurements of the internal state of a digitalprinting press as well as of the densities of monochrome patches. Thispatent application does neither teach how to obtain ink thicknesscontrol parameters from polychromatic halftone patches nor fromhalftones being part of the actual printed document pages.

U.S. Pat. No. 7,000,544, (Measurement and regulation of inking in webprinting, to Riepenhoff, filed 1^(st) Jul. 2002) teaches a process formeasuring the mean spectrum integrated over a stripe of the printedsheet. It also teaches a device for regulating the ink density bypredicting the mean reflection spectrum along a stripe thanks to acorrespondence function between image data located along the stripe andthe resulting reflection spectrum. That correspondence function does notincorporate an explicit ink thickness variable, nor does it make thedistinction between nominal surface coverages and effective surfacecoverages. It therefore does not account for the ink spreadingphenomenon.

U.S. Pat. No. 7,252,360, Ink thickness variations for the control ofcolor printers, filed 25^(th) Oct. 2005, issued 7^(th) of Aug. 2007, toR. D. Hersch (also inventor in the present patent application), P.Amrhyn and M. Riepenhoff, teaches a spectral prediction model fordeducing ink thickness variations working with a single headspectrophotometer located on the running printing press, for acquiringhalftones or mean reflection spectra over stripes (spectral acquisitionaveraged over the length of a print). The present invention improvesupon U.S. Pat. No. 7,252,360, by replacing the single moving headspectrophotometer by a sensing system formed by non-movingmultiple-channel solid-state high-speed acquisition sensor devicesreplicated over the width of the printer (printed sheet width). Solidstate sensor devices, especially when embodied by Single PhotonAvalanche Diodes, provide a cheaper solution, compared with a movinghead spectrophotometer. In addition, in the present invention, thehigh-speed sensor response enables sensing small halftone area segmentswhich do not incorporate much paper white and exhibit therefore lessnoise. Furthermore, the new online calibration steps are performed onthe running press and do not require specially printed uniform colorpatches or control stripes.

The present disclosure provides a robust means of deducing online and inreal time ink thickness or ink volume variations of cyan, magenta,yellow and black on a running printing press or color printer, withoutneeding at print time specific solid or halftone patches within theprinted sheet. In addition, due to an optional online calibration, thededuced ink thickness variations are accurate in respect to the currentprinting device operating conditions (temperature, settings of theprinting device, etc. . . . ).

SUMMARY

The present invention proposes a method and a computing system fordeducing ink thickness variations from multi-channel sensor responsesacquired online during print operation of a printing press or a printer.Acquiring the ink thickness variations online and in real-time enablesregulating the ink deposition process during normal print operation.Real-time online control of the ink deposition process enables keeping ahigh color accuracy from print sheet to print sheet and from print jobto print job. This is especially important if the ink deposition processis not stable when working in open loop mode.

Ink thickness variations are expressed as ink thickness variationfactors incorporated into an ink thickness variation and sensor responseenhanced spectral prediction model. The method for computing inkthickness variations comprises both calibration and ink thicknessvariation computation steps. The calibration steps comprise themeasurement and adjustment of paper reflectance, possibly thecalculation of internal paper reflectance, the calculation of inktransmittances from measured reflectances, the computation of scalar inkthicknesses of solid superposed inks and, in order to account for inkspreading, the computation of effective surface coverages of single inkhalftones in different superposition conditions. By interpolation, weobtain the effective surface coverage curves mapping nominal toeffective surface coverages of single ink halftones in differentsuperposition conditions. The calibration steps can be divided intooffline and online calibration steps. The offline calibration stepsrequire specially printed patches such as solid ink and solid inksuperposition patches on which spectral reflectance measurements areperformed. From these spectral reflectance measurements, the internalreflectance of paper and the transmittance of the inks are obtained. Theoptional online calibration steps improve the calibration in case ofchanges in the printer operating conditions, e.g. a change intemperature, a change of paper, or a new set of inks which differs fromthe previous set. Online calibration steps are performed only withmulti-channel sensor responses from printed area segments located withinthe printed sheet. They may comprise the recalibration of the paperreflectance, and possibly the calibration or recalibration of theeffective surface coverage curves. They may also comprise deducingreference thickness variations which are then used to compute thicknessvariations normalized in respect to these reference thicknessvariations.

In respect to the ink thickness variation computation steps, thethickness variation and sensor response enhanced spectral predictionmodel comprises as solid colorant transmittance of two or moresuperposed solid inks the transmittance of each of the contributingsuperposed ink raised to the power of a product of two variables, onevariable being the superposition condition dependent ink thickness andthe other variable being the ink thickness variation factor. The inkthickness variations are fitted by minimizing a distance metric betweenpredicted multi-channel sensor responses and acquired multi-channelsensor responses, the predicted multi-channel sensor responses beingcomputed according to the ink thickness variation and sensor responseenhanced spectral prediction model.

With one of the multi-sensor channels also operating in the nearinfra-red region, for black inks absorbing in the near infra-red region,the ambiguity between ink thickness variations of the black ink andjoint ink thickness variations of the cyan, magenta, and yellow inks isresolved.

In case that the area sensed by the multi-sensor devices comprisessignificantly different colors, the obtained sensor response is a meanvalue over sensor responses across several nearly uniform colorsub-areas. Corresponding predicted sensor responses can be computed bypredicting sub-areas sensor responses and by performing a weightedaverage over these sub-area sensor responses, the weights correspondingto the respective surface coverages of the sub-areas.

If the nominal surface coverages of the halftone area segment on whichthickness variations are to be performed are unknown, it is possible, inaddition to the calibration of the transmittances and the thicknesses ofthe inks, to measure sensor responses from a reference print underreference settings and to deduce with the thickness enhanced spectralprediction model the corresponding reference effective surfacecoverages. The sensor responses are then predicted with the deducedreference effective surface coverages. Ink thickness variations arecomputed by minimizing a distance metric between predicted sensorresponses and measured sensor responses. The computed ink thicknessvariations represent ink thickness variations in respect to thereference print.

The disclosed ink thickness variation computing system computes inkthickness variations online and in real time. It comprises multi-channelsensor devices, a processing module, and a computing system. Themulti-channel sensor devices are replicated over the width of the printsheet. The multi-channel sensor devices respond at different spectralsensibility ranges within the visible and near infra-red wavelengthrange. The multi-channel sensor devices, due to their high-speedacquisition capabilities, provide responses according to the reflectanceof small areas within a print sheet. The processing module accumulatesthe digital sensor responses and forwards them to the computing system,which according to an ink thickness variation and sensor responseenhanced spectral prediction model deduces the ink thickness variations.

In a preferred embodiment, the sensor devices are Single PhotonAvalanche Diodes, which create a pulse upon arrival of a photon. Withpulse dead times in the order of 20 ns to 50 ns it is possible to have amaximal photon count between 20000 and 50000 pulses per millisecond.This allows to have both low sensor acquisition times (e.g. 0.2 ms to 1ms) and a high signal to noise ratio. At a printer speed of 10 m/s, thearea segment length passing underneath a sensor has a correspondinglength of 2 mm to 10 mm. In a possible layout, there may be one colored,respectively infra-red, LED in front of each sensor with the light ofthe LED being directed towards the print and being reflected into thecorresponding sensor. The colored and infra-red LED's may also bereplaced by a white LED followed by a corresponding colored,respectively infra-red, filter. To avoid specular reflection, theincident light may be oriented towards the print at 45 degrees and readout at zero degrees. Alternately, to discard specular reflections, it isalso possible to have a first polarizer on the incident light path andsecond polarizer turned by 90 degrees in respect to first one on thereflected light path.

In a further possible layout of the illumination and sensing system, thesensing system may be formed by the multi-channel sensors located withina single integrated circuit. The illumination may be produced by a whiteLED whose light is directed towards the print. The reflected light isfor example filtered by specific filters each located in front of itsrespective sensor.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a schematic view of an ink thickness variation computationmodel embodiment, where ink thickness variations dr_(C), dr_(M), dr_(Y)are deduced from known nominal surface coverages of cyan (c), magenta(m), and yellow (y) inks and from sensor responses q_(r), q_(g), q_(b);

FIG. 2 illustrates a generalization of the ink thickness variationcomputation model of FIG. 1, for a set of 4 inks with nominal inputsurface coverages c₁, c₂, c₃, c₄, 4-channel sensor responses q_(α),q_(β), q_(γ), q_(δ) and output ink thickness variations dr₁, dr₂, dr₃,dr₄;

FIG. 3A shows a sensing system comprising 4-channel illuminating/sensordevices replicated over the width of the printed sheet and theircorresponding input and output signals;

FIG. 3B shows a sensor processing module comprising a multiplexer, acounter, fast logic (FL) and a microcontroller (μC);

FIG. 4A shows a 4 channel illuminating/sensing device set and itscorresponding input and output signals;

FIG. 4B shows one integrated circuit comprising a 4 channel sensingdevice set, pulse counters and a multiplexer;

FIG. 5A shows an embodiment of a single illuminating/sensing device withan incident angle of 45° and a light capture angle of 0°;

FIG. 5B shows a further embodiment of a single illuminating/sensingdevice comprising a light-emitting diode (LED), a polarizing filter 514on the incident light path, a beam splitter 510 and a second polarizingfilter 511 on the reflected light path;

FIG. 5C shows a further embodiment with a white diffuse illumination 534illuminating the print sheet 537 and a sensing device 533 whosefocalizing lens 531 is coated with a filtering substance 530.

FIG. 6 shows a possible embodiment of blue, green, red and infra-redsensor sensibilities;

FIG. 7 shows an ink thickness variation computing system comprising asensing system 708, a computing system 701 and a print actuationparameter driving module 709; and

FIGS. 8A and 8B illustrate respectively examples of deduced normalizedink thickness variations of the magenta, respectively the black ink inmany different print trials, where the ink feed of one or of severalinks has been increased or decreased.

DETAILED DESCRIPTION OF THE INVENTION

The present invention proposes models, a computing system as well asmethods for deducing ink thickness variations from sensor responsesobtained on a printer or printing press, online and in real-time. Thecomputed ink thickness variations enable controlling the ink depositionand therefore the color accuracy, in the case of high-speed printingpresses, of network printers and desktop printers. The ink thicknessvariations can be directly used for the real-time control of the printactuation parameters which influence the ink deposition, such as the inkfeed in the case of an offset press.

The proposed method and computing system rely on a spectral predictionmodel incorporating as input parameters the responses from multi-channelsensors, as internal parameters the ink thicknesses and as outputparameters ink thickness variation factors. Hereinafter, such a model iscalled “thickness variation and sensor response enhanced spectralprediction model”. Ink thickness variations are deduced by an “inkthickness variation computation model”. When the ink thickness variationcomputation model is embodied by a computing system, it becomes an “inkthickness variation computing system”. By deriving from the thicknessvariation computation model a series of processing steps, we obtain athickness variation prediction method.

In the present invention, unknown variables are fitted by minimizing adistance metric (also called difference metric) between a measuredreflection spectrum, respectively sensor responses, and a reflectionspectrum, respectively sensor responses predicted according to aspectral reflectance prediction model. The preferred distance metric isthe sum of square differences between the corresponding measured andpredicted reflection density spectra, respectively sensor densityresponses, with reflection density spectra, respectively sensor densityresponses, being computed according to formula (2a), respectively (2b).Minimizing a distance metric can be performed, for example with asoftware package such as Matlab or with a program implementing Powell'sfunction minimization method (see W. H. Press, B. P. Flannery, S. A.Teukolsky, W. T. Fetterling, Numerical Recipes, Cambridge UniversityPress, 1st edition, 1988, section 10.5, pp. 309-317).

The present invention deals with deducing ink thickness variations fromsensor responses of illuminated halftones with color inks. The substrateon which the inks are printed is paper in the general case. But in othercases, the substrate can be another diffusely reflecting substrate suchas a polymer. In the present invention, the term “paper” is meant in ageneric sense and designates any diffusely reflecting substrate.

Once printed, the physical size of the printed dot generally increases,partly due to the interaction between the ink and the paper, and partlydue to the interaction between successively printed ink layers. Thisphenomenon is called physical (or mechanical) dot gain or ink spreading.Therefore, “nominal surface coverages” (or simply “nominal coverages”)are initially specified amounts of inks and “effective surfacecoverages” (or simply “effective coverages”) are physical surfacecoverages inferred from the spectral or sensor response measurements ofthe printed patches according to the considered spectral predictionmodel.

Halftones which are printed with multiple, partly superposed inks arecalled polychromatic halftones. A solid ink patch is a patch printedwith 100% surface coverage. A halftone is a printed area, e.g. a smallrectangle within a printed sheet, where at least one ink layer isprinted in halftone. Halftones may form an integral part of a printeddocument page delivered to a customer, i.e. they may be located withincolor images, within gray or colored bars separating different parts ofa printed document page, or they may form the gray or colored backgroundof advertisements.

A calibration halftone patch is a uniform color patch where one ink isprinted as a halftone at a specified nominal surface coverage value, forexample 25%, 50% or 75%. This halftone may be printed alone on paper orprinted in superposition with other solid inks. Note that since one ofthe goals of the present invention is to avoid printing special controlstripes or halftone patches at the borders of a printed document page,the disclosed online calibration does not require calibration halftonepatches.

A printed area segment may be located within a printed page. The printedarea segment is a rectangle whose length corresponds to a smalldisplacement of a print page location under a sensor. The width of therectangle corresponds to the width of the sensor.

The considered inks are usually the standard cyan, magenta, yellow andblack inks. But the disclosed ink thickness variation computation modelmay also be applied in a straightforward manner to inks of other colors.For example, the set of inks may comprise the standard cyan, magenta andyellow inks plus one or several additional inks such as orange, red,green and blue. The term “ink” is used in a generic sense: It maycomprise any colored matter that can be transferred onto specificlocations of a substrate (e.g. offset inks, ink-jet inks, tonerparticles, liquid toner, dye sublimation colorants, etc. . . . ).

In the present invention, the multi-channel sensors replicated over thewidth of the printed sheet comprise for each channel an illuminating andsensor device, also called “illuminating/sensor device”. In the case ofmultiple channels, we have a “set of illuminating/sensor devices” orsimply an “illuminating/sensor set”. When such an illuminating/sensorset is replicated over the width the print, it is called“illuminating/sensor array”. An illuminating/sensor set may comprise oneilluminating device and several sensors.

Throughout the application the expressions “printing device”, “printer”and “printing press” are used interchangeably, i.e. the disclosure withrespect to one is equally applicable with respect to the other. Theinvention is advantageous for computing ink thickness variations orequivalently, ink colorant concentration variations by a computingsystem which regulates the print actuation parameters controlling theamount of deposited colorant substance or ink, such as the ink feed (inkvolume), the ink thickness, or the ink colorant concentration.

The present invention also enables controlling the ink deposition inprinters, such as electro-photographic printers, ink-jet printers,solid-tone printers, liquid-toner printers, dye sublimation printers andthermal transfer printers. In such printers, there is often thepossibility of varying the size of the individual printed dot. Thenumber of available dot sizes depends on the printer technology, and mayrange from 3 to 255 different dot sizes. Increasing, respectivelydecreasing, the amount of ink can also be achieved by increasing,respectively decreasing, the individual printed dot size.

For a printing press (e.g. a web-offset press), deducing ink thicknessvariations from sensor responses enables the automatic regulation of thethickness (or volume) of the deposited inks by acting on the printactuation parameters such as the ink feed. For a digital printer hookedonto a computer network or for a desktop printer, deduction of inkthickness variations enables adjusting the printer settings by acting onthe print actuation parameters, such as the droplet ejection mechanismin the case of an ink-jet printer, the electronic charge and dischargemechanism as well as possibly the fusing mechanism in the case of anelectrophotographic printer, and the head element temperature profilesin the case of thermal transfer or dye sublimation printers.

Deducing the thickness variations of the inks from sensor responses ofilluminated halftones is achieved thanks to an enhanced spectralreflectance prediction model which has an explicit representation of thewavelength-dependent ink transmittances, of the wavelength-dependentreflectance of paper, of the wavelength-dependent sensibilities of eachof the multi-channel sensor devices, of wavelength-independent inkthicknesses, and of wavelength-independent ink thickness variations.This ink thickness and sensor response enhanced spectral reflectanceprediction model takes into account ink spreading, i.e. the mapping fromnominal to effective dot surface coverages under different inksuperposition conditions.

The embodiment of the disclosed ink thickness variation computationmodel presented here uses as base spectral prediction model either theClapper-Yule spectral reflection prediction model or the Yule-Nielsenmodified spectral Neugebauer model, see D. R. Wyble, R. S. Berns, ACritical Review of Spectral Models Applied to Binary Color Printing,Journal of Color Research and Application, Vol. 25, No. 1, 4-19, 2000,hereinafter referenced as [Wyble and Berns 2000].

The Clapper-Yule model, see F. R. Clapper, J. A. C Yule, “The effect ofmultiple internal reflections on the densities of halftone prints onpaper”, Journal of the Optical Society of America, Vol. 43, 1953,600-603, hereinafter referenced as [Clapper53], takes simultaneouslyinto account halftone patterns and multiple internal reflectionsoccurring at the interface between the paper and the air and assumes arelatively high screen frequency. In a recent extension, theClapper-Yule model has been combined with a Saunderson correctedspectral Neugebauer model which gives assumes a low screen frequency,see R. D. Hersch and al, “Spectral reflection and dot surface predictionmodels for color halftone prints”, R. D. Hersch, et. al., Journal ofElectronic Imaging, Vol. 14, No. 3, August 2005, pp. 33001-12,incorporated in the present disclosure by reference, hereinafterreferenced as [Hersch05A]. The weighting factor b indicates the relativeweight of the Saunderson corrected Neugebauer model component. For fourink prints, this composed Clapper-Yule Saunderson corrected Neugebauerspectral reflection prediction model, hereinafter referenced as “CYSNspectral prediction model” is formulated as follows: $\begin{matrix}{{R(\lambda)} = {{K*r_{s}} + {\left( {1 - r_{s}} \right)*{r_{g}(\lambda)}*{\left( {1 - r_{i}} \right) \cdot \begin{bmatrix}{{{b \cdot \quad{\sum\limits_{j\quad = \quad 1}^{\quad 16}\quad\frac{\quad{a_{\quad j}*\quad{\quad{t_{\quad j}(\lambda)}}^{2}}}{\quad{1\quad - \quad{r_{\quad g}(\lambda)*\quad r_{\quad i}*\quad t_{\quad j}^{\quad 2}(\lambda)}}}}}\quad +}\quad} \\{\left( {1\quad - \quad b} \right) \cdot \quad\frac{\quad\left( \quad{\sum\limits_{j\quad = \quad 1}^{\quad 16}\quad{a_{\quad j}*\quad t_{\quad j}(\lambda)}} \right)^{2}}{\quad{1\quad - \quad{r_{\quad g}(\lambda)*\quad r_{\quad i}*\quad{\sum\limits_{j\quad = \quad 1}^{\quad 16}\quad{a_{\quad j}*\quad t_{\quad j}^{\quad 2}(\lambda)}}}}}}\end{bmatrix}}}}} & \left( {1a} \right)\end{matrix}$where K is the fraction of specular reflected light reaching thespectrophotometer (for a 45/0 degrees measuring geometry, K=0), r_(s) isthe surface reflection at the air paper coating interface, r_(g) is thepaper substrate reflectance, r_(i) is the internal Fresnel reflectionfactor obtained by integrating the Fresnel reflection factor over allorientations, a_(j) represents the fractional surface coverage of acolorant j, t_(j) represents the transmittance of a colorant j, and R(λ)is the predicted reflection spectrum. The b weighting factor is fittedfor a giving printing process by minimizing on a subset of halftones adifference metric between predicted reflection spectrum and measuredreflection spectrum. At a screen frequency (screen ruling) above 120 lpi(lines per inch), experience shows that b tends to zero, i.e. theClapper-Yule component of the model is sufficient and provides a highenough accuracy.

Instead of using the Clapper-Yule Saunderson corrected Neugebauer model(CYSN) as base spectral reflectance model, one may equally well use theYule-Nielsen modified spectral Neugebauer model (YNSN) extended witheffective coverages in different superposition conditions (see R. DHersch and al, “Improving the Yule-Nielsen modified spectral Neugebauermodel by dot surface coverages depending on the ink superpositionconditions”, IS&T/SPIE Electronic Imaging Symposium, Conf. Imaging X:Processing, Hardcopy and Applications, January 2005, SPIE Vol. 5667,434-445, incorporated by reference) where reflection spectra of thecolorants R_(j) are expressed by colorant transmittance spectra t_(i)and the paper reflectance R_(g), as expressed in Eq. (1b).

For 4 inks, the corresponding Yule-Nielsen modified Spectral Neugebauerreflectance is $\begin{matrix}{{{{R(\lambda)} = \left( {\sum\limits_{j = 1}^{16}{a_{j} \cdot {R_{j}(\lambda)}^{\frac{1}{n}}}} \right)^{n}};}{with}} & \left( {1b} \right) \\{{R_{j}(\lambda)} = {{t_{j}(\lambda)}^{2}*{R_{g}(\lambda)}}} & \left( {1c} \right)\end{matrix}$where the Yule-Nielsen scalar n-value is fitted for a giving printingprocess by minimizing on a subset of halftones a difference metricbetween predicted reflection spectrum and measured reflection spectrum.Reflectances R_(j) (λ) are measured reflectances of paper (R_(g)), ofsolid inks and of solid ink superpositions printed on paper. In the YNSNmodel, there is no need to derive an internal paper reflectance from ameasured paper reflectance.

The reflection density spectrum D(λ) is deduced from the reflectanceR(λ) according to the following well known formulaD(λ)=−log₁₀(R(λ))   (2a)

Equations (1a), (1b) define respectively two different embodiments ofbase spectral prediction models. For each embodiment, either thereflection spectrum R(λ) or the reflection density spectrum D(λ) can bepredicted.

In the present invention, instead of a spectral acquisition device(spectrophotometer), we consider for online use sensor acquisitiondevices such as blue, green, red and near-infra-red sensors. The CYSN orYNSN spectral prediction models given above can be extended to predictthe response of the sensors.

In the case of 4 α, β, γ, δ illuminating and sensor devices havingrespective illuminant spectra I_(α), I_(β), I_(γ), I_(δ), and spectralsensitivities S_(α), S_(β), S_(γ), S_(δ), the responses of the α, β, γ,δ sensors expressing the amount of light reflected by the sample ofspectral reflectance R can be described by Equations (3). In theseequations, all spectral values are discrete values, distributed acrossthe wavelength range of interest, e.g. between 380 nm and preferably 900nm for the visible wavelength and near infra-red wavelength range. Thedifferences in sensibility between channels α, β, γ, δ may be due todifferent illuminations (e.g. blue, green, red, and infra-redilluminations expressed by I_(α), I_(β), I_(γ), I_(δ)) or due to filterslocated in the pathway of the light to the sensors, expressed ascombined filter and sensor sensibilities S_(α), S_(β), S_(γ), S_(δ).$\begin{matrix}{{q_{\alpha} = {\sum\limits_{i}{S_{\alpha\quad i}R_{i}{I_{\alpha\quad i}/{\sum\limits_{i}{S_{\alpha\quad i}I_{\alpha\quad i}}}}}}}{q_{\beta} = {\sum\limits_{i}{S_{\beta\quad i}R_{i}{I_{\beta\quad i}/{\sum\limits_{i}{S_{\beta\quad i}I_{\beta\quad i}}}}}}}{q_{\gamma} = {\sum\limits_{i}{S_{\gamma\quad i}R_{i}{I_{\gamma\quad i}/{\sum\limits_{i}{S_{\gamma\quad i}I_{\gamma\quad i}}}}}}}{q_{\delta} = {\sum\limits_{i}{S_{\delta\quad i}R_{i}{I_{\delta\quad i}/{\sum\limits_{i}{S_{\delta\quad i}I_{\delta\quad i}}}}}}}} & {{Equation}\quad(3)}\end{matrix}$

By plugging the predicted reflectance R(λ) of Eq. (1a) or (1b) asdiscrete reflectance vector components R_(i) into equations (3), thesensor responses q_(α), q_(β), q_(γ), q_(δ), are predicted as a functionof the surface coverages a_(j) of the colorants. One may also considerconverting the sensor responses q_(k) into sensor densities responsesD_(k) according to the equationD _(k)=−log₁₀(q _(k))   (2b)

The well known Demichel equations (4) yield the colorant (also calledNeugebauer primaries) surface coverages a_(i) as a function of the inksurface coverages c₁, c₂, c₃, and c₄ of the inks i₁, i₂, i₃, and i₄.i ₁ alone: a ₁ =c ₁(1−c ₂)(1−c ₃)(1−c ₄)i ₂ alone: a ₂=(1−c ₁)c ₂(1−c ₃)(1−c ₄)i ₃ alone: a ₃=(1−c ₁)(1−c ₂)c ₃(1−c ₄)i ₄ alone: a ₄=(1−c ₁)(1−c ₂)(1−c ₃)c ₄i ₁ and i ₂ : a ₅ =c ₁ c ₂(1−c ₃)(1−c ₄)i ₁ and i ₃ : a ₆ =c ₁(1−c ₂)c₃(1−c ₄)i _(i) and i ₄ : a ₇ =c ₁(1−c ₂)(1−c ₃)c ₄i ₂ and i ₃ : a ₈=(1−c ₁)c ₂ c ₃(1−c ₄)i ₂ and i ₄ : a ₉=(1−c ₁)c ₂(1−c ₃)c ₄i ₃ and i ₄ : a ₁₀=(1−c ₁)(1−c ₂)c ₃ c ₄i ₁ , i ₂ and i ₃ : a ₁₁ =c ₁ c ₂ c ₃(1−c ₄)i ₂ , i ₃ and i ₄ : a ₁₂=(1−c ₁)c ₂ c ₃ c ₄i _(i) , i ₃ and i ₄ : a ₁₃ =c ₁(1−c ₂)c ₃ c ₄i _(i) , i ₂ and i ₄ : a ₁₄ =c ₁ c ₂(1−c ₃)c ₄i ₁ , i ₂ , i ₃ and i ₄ : a ₁₅ =c ₁ c ₂ c ₃ c ₄substrate white: a ₁₆=(1−c ₁)(1−c ₂)(1−c ₃)(1−c ₄).   Equations (4)

For more information on the computation of the colorant surfacecoverages from ink surface coverages, see [Wyble and Berns 2000].

Let us consider the Clapper-Yule based spectral prediction model. Byinserting the relative amounts of colorants a_(i) and theirtransmittances t_(i) into Equation (1), we obtain a predicted reflectionspectrum of a color patch printed with given surface coverages of cyan,magenta, yellow and black. Both the specular reflection r_(s) and theinternal reflection r_(i) depend on the refraction indices of the air(n₁=1) and of the paper (n₂=1.5 for paper). According to the Fresnelequations (see E. Hecht, Schaum's Outline of Optics, McGraw-Hill, 1974,Chapter 3), for collimated light at an incident angle of 45°, thespecular reflection factor is r_(s)=0.05. With light diffusely reflectedby the paper (Lambert radiator), the internal reflection factor isr_(i)=0.6 (see D. B. Judd, Fresnel reflection of diffusely incidentlight, Journal of Research of the National Bureau of Standards, Vol. 29,November 42, 329-332). To put the model into practice, we deduce fromEquation (1a) the internal reflectance spectrum r_(g) of a blank paperby setting all the ink surface coverages different from white as zero$\begin{matrix}{r_{g} = \frac{R_{g} - {K*r_{S}}}{1 + {\left( {1 - K} \right)*r_{i}*r_{S}} + {r_{i}*R_{g}} - {r_{S}r_{i}}}} & (5)\end{matrix}$where R_(g) is the measured unprinted paper reflectance.

We then calculate the transmittance of each individual solid colorant(solid inks and solid ink superposition) t_(c), t_(m), t_(y), t_(k),t_(cm), t_(cy), t_(ck), t_(my), t_(mk), t_(yk), t_(cmy), t_(myk),t_(cyk), t_(cmk), t_(cmyk), t_(w) by inserting into Eq. (1a) themeasured solid colorant reflectance R_(i) and by setting the appropriatecolorant surface coverage a_(i)=1 and all other colorant coveragesa_(j≠i)=0. The transmittance of solid colorant i becomes $\begin{matrix}{t_{i} = \sqrt{\frac{R_{i} - {K*r_{S}}}{{r_{g}*r_{i}*\left( {R_{i} - {K*r_{S}}} \right)} + {r_{g}*\left( {1 - r_{i}} \right)*\left( {1 - r_{S}} \right)}}}} & (6)\end{matrix}$

We should also take ink spreading into account, i.e. the increase ineffective (physical) dot surface coverage. We can fit effective surfacecoverages either by minimizing a distance metric either between measuredand predicted reflection spectra or between measured and predictedmulti-channel sensor responses.

During an initial calibration, for each ink u, we fit according to theselected spectral prediction model (CYSN, Eq. (1a) or YNSN, Eq. (1b),with a_(j=u) being fitted and a_(j≠u)=0) the unknown effective surfacecoverages f_(u)(c_(u)) of the measured single ink patches at nominalcoverages c_(u) of e.g. 25%, 50%, 75%, 100% by minimizing a distancemetric between predicted and measured reflection spectra ormulti-channel sensor responses.

Similarly, we fit the unknown effective surface coverages f_(u/v)(c_(u))of single ink halftones of ink u printed in superposition with a secondsolid ink v at nominal surface coverages c_(u) (e.g. at 25%, 50% and75%) with the selected spectral prediction model, Eq. (1a) or (1b), withhalftone surface coverage f_(u/v)(c_(u))=a_(u) being fitted, a secondsolid ink a_(v)=1 and all other colorant surface coveragesa_((j≠u,j≠v))=0, by minimizing a distance metric between predicted andmeasured reflection spectra, respectively multi-channel sensorresponses. The same procedure is applied for fitting the unknowneffective surface coverages f_(u/vw)(c_(u)) of single ink halftonesa_(u) printed in superposition with two solid inks, Eq. (1a) or (1b),with halftone surface coverage f_(u/vw)(c_(u))=a_(j=u) being fitted, asecond solid ink a_(v)=1, a 3^(rd) solid ink a_(w)=1 and 4^(th) inksurface coverage a_((j≠u,j≠v,j≠w))=0. The same procedure is also appliedfor fitting the unknown effective surface coverages f_(u/vwz)(c_(u)) ofsingle ink halftones of ink u printed in superposition with three solidinks, Eq. (1a) or (1b), with halftone surface coveragef_(u/vwz)(c_(u))=a_(j=u) being fitted, a second solid ink a_(v)=1, a3^(rd) solid ink a_(w)=1 and a 4^(th) solid ink a_(z)=1. Each set offitted effective surface coverages (e.g. at nominal surface coveragesc_(u)=25%, 50% and 75%) maps nominal surface coverages to effectivesurface coverages for that superposition condition. For a givensuperposition condition, by interpolating between the known mappingsbetween nominal to effective surface coverages, we obtain a functionmapping between nominal to effective surface coverages. This function iscalled “effective surface coverage curve” or “effective coverage curve”.

In order to obtain the effective surface coverages c₁, c₂, c₃ and c₄ ofa color halftone patch from their nominal coverages c_(1n), c_(2n)c_(3n), and c_(4n) and then, with the Demichel equations (4), to obtainthe corresponding effective colorant surface coverages a_(j) to beinserted in the spectral prediction model equation (1a), or respectively(1b), it is necessary to weight the contributions of the correspondingeffective coverage curves. The weighting functions depend on theeffective coverages of the considered ink alone, of the considered inkin superposition with a second ink, of the considered ink insuperposition with the two other inks and of the considered ink insuperposition with the three other inks. For the considered system of 4inks i₁, i₂, i₃ and i₄ with nominal coverages c_(1n) c_(2n), c_(3n) andc_(4n) and effective coverages c₁, c₂, c₃ and c₄, assuming that inks areprinted independently of each other, e.g. according to the classicalscreen angles 15°, 45°, 75° and 0°, by computing the relative weight,i.e. the relative surface of each superposition condition, we obtain thesystem of equations (7) published in [Hersch05A]. $\begin{matrix}{{c_{1} = {{f_{1}\left( c_{1\quad n} \right)\left( {1 - c_{2}} \right)\left( {1 - c_{3}} \right)\left( {1 - c_{4}} \right)} + {f_{\quad{1|2}}\left( c_{1\quad n} \right)c_{2}\left( {1 - c_{3}} \right)\left( {1 - c_{4}} \right)} + {f_{\quad{1|3}}\left( c_{1\quad n} \right)\left( {1 - c_{2}} \right)c_{3}\left( {1 - c_{4}} \right)} + {f_{\quad{1|4}}\left( c_{1\quad n} \right)\left( {1 - c_{2}} \right)\left( {1 - c_{3}} \right)c_{4}} + {f_{\quad{1|23}}\left( c_{1\quad n} \right)c_{2}c_{3}\left( {1 - c_{4}} \right)} + {f_{\quad{1|24}}\left( c_{1\quad n} \right)c_{2}\left( {1 - c_{3}} \right)c_{4}} + {f_{\quad{1|34}}\left( c_{1\quad n} \right)\left( {1 - c_{2}} \right)c_{3}c_{4}} + {f_{\quad{1|234}}\left( c_{1\quad n} \right)c_{2}c_{3}c_{4}}}}{c_{1} = {{f_{2}\left( c_{2\quad n} \right)\left( {1 - c_{1}} \right)\left( {1 - c_{3}} \right)\left( {1 - c_{4}} \right)} + {f_{\quad{2|1}}\left( c_{2\quad n} \right)c_{1}\left( {1 - c_{3}} \right)\left( {1 - c_{4}} \right)} + {f_{\quad{2|3}}\left( c_{2\quad n} \right)\left( {1 - c_{1}} \right)c_{3}\left( {1 - c_{4}} \right)} + {f_{\quad{2|4}}\left( c_{2\quad n} \right)\left( {1 - c_{1}} \right)\left( {1 - c_{3}} \right)c_{4}} + {f_{\quad{2|13}}\left( c_{2\quad n} \right)c_{1}c_{3}\left( {1 - c_{4}} \right)} + {f_{\quad{2|24}}\left( c_{2\quad n} \right)c_{1}\left( {1 - c_{3}} \right)c_{4}} + {{f_{\quad{2|34}}\left( c_{2\quad n} \right)}\left( {1 - c_{1}} \right)c_{3}c_{4}} + {{f_{\quad{2|134}}\left( c_{2\quad n} \right)}c_{1}c_{3}c_{4}}}}{c_{3} = {{f_{3}\left( c_{3\quad n} \right)\left( {1 - c_{1}} \right)\left( {1 - c_{2}} \right)\left( {1 - c_{4}} \right)} + {f_{\quad{3|1}}\left( c_{3\quad n} \right)c_{1}\left( {1 - c_{2}} \right)\left( {1 - c_{4}} \right)} + {f_{\quad{3|2}}\left( c_{3\quad n} \right)\left( {1 - c_{\quad}} \right)c_{2}\left( {1 - c_{4}} \right)} + {f_{\quad{3|4}}\left( c_{3\quad n} \right)\left( {1 - c_{1}} \right)\left( {1 - c_{2}} \right)c_{4}} + {f_{3|12}\left( c_{3\quad n} \right)c_{1}c_{2}\left( {1 - c_{4}} \right)} + {f_{3|14}\left( c_{3\quad n} \right)c_{1}\left( {1 - c_{2}} \right)c_{4}} + {f_{3|24}\left( c_{3\quad n} \right)\left( {1 - c_{1}} \right)c_{2}c_{4}} + {{f_{\quad{3|124}}\left( c_{3\quad n} \right)}c_{1}c_{2}c_{4}}}}{c_{4} = {{f_{4}\left( c_{4\quad n} \right)\left( {1 - c_{1}} \right)\left( {1 - c_{2}} \right)\left( {1 - c_{3}} \right)} + {f_{4|1}\left( c_{4\quad n} \right)c_{1}\left( {1 - c_{2}} \right)\left( {1 - c_{3}} \right)} + {f_{4|2}\left( c_{4\quad n} \right)\left( {1 - c_{1}} \right)c_{2}\left( {1 - c_{3}} \right)} + {f_{4|3}\left( c_{4\quad n} \right)\left( {1 - c_{1}} \right)\left( {1 - c_{2}} \right)c_{3}} + {f_{4|12}\left( c_{4\quad n} \right)c_{1}c_{2}\left( {1 - c_{3}} \right)} + {f_{4|13}\left( c_{4\quad n} \right)c_{1}\left( {1 - c_{2}} \right)c_{3}} + {f_{4|23}\left( c_{4\quad n} \right)\left( {1 - c_{1}} \right)c_{2}c_{3}} + {{f_{4|123}\left( c_{4\quad n} \right)}c_{1}c_{2}{c_{3}.}}}}} & {{Equation}\quad(7)}\end{matrix}$

This system of equations requires the acquisition of 32 effectivecoverage curves (all f functions). In the case of cyan, magenta, yellowand black inks, this system of equations may be simplified by assumingthat any halftone printed on the solid black ink results anyway in acolor very close to black and does not modify the ratio between theweights of the effective surface coverage curves of that halftone. Forblack ink halftones however, the surface coverage curves depend on thedifferent superposition conditions and are therefore kept intact. Wetherefore obtain for cyan, magenta, yellow and black inks the simplifiedset of effective surface coverage equations (8), mapping nominal surfacecoverages c_(n) m_(n), y_(n) and k_(n) to effective surface coverages c,m, y and k. $\begin{matrix}{{c = {{f_{c}\left( c_{n} \right)\left( {1 - m} \right)\left( {1 - y} \right)} + {f_{\quad{c|m}}\left( c_{n} \right)m\left( {1 - y} \right)} + {f_{c|y}\left( c_{n} \right)\left( {1 - m} \right)y} + {{f_{c|{my}}\left( c_{n} \right)}m\quad y}}}{m = {{{f_{m}\left( m_{n} \right)}\left( {1 - c} \right)\left( {1 - y} \right)} + {{f_{\quad{m|c}}\left( m_{n} \right)}{c\left( {1 - y} \right)}} + {{f_{\quad{m|y}}\left( m_{n} \right)}\left( {1 - c} \right)y} + {{f_{\quad{f|{cy}}}\left( m_{n} \right)}c\quad y}}}{y = {{{f_{y}\left( y_{n} \right)}\left( {1 - c} \right)\left( {1 - m} \right)} + {{f_{\quad{y|c}}\left( y_{n} \right)}{c\left( {1 - m} \right)}} + {{f_{\quad{y|m}}\left( y_{n} \right)}\left( {1 - c} \right)m} + {{f_{\quad{y|{cm}}}\left( y_{n} \right)}c\quad m}}}{k = {{{f_{k}\left( k_{n} \right)}\left( {1 - c} \right)\left( {1 - m} \right)\left( {1 - y} \right)} + {{f_{k|c}\left( k_{n} \right)}{c\left( {1 - m} \right)}\left( {1 - y} \right)} + {{f_{k|m}\left( k_{n} \right)}\left( {1 - c} \right){{m\left( {1 - y} \right)}++}{f_{k|y}\left( k_{n} \right)}\left( {1 - c} \right)\left( {1 - m} \right)y} + {{f_{k|{cm}}\left( k_{n} \right)}c\quad{m\left( {1 - y} \right)}} + {{f_{k|{cy}}\left( k_{n} \right)}{c\left( {1 - m} \right)}y} + {{f_{k|{my}}\left( k_{n} \right)}\left( {1 - c} \right)m\quad y} + {{f_{k|{cmy}}\left( k_{n} \right)}c\quad m\quad{y.}}}}} & {{Equation}\quad(8)}\end{matrix}$

Here, only 20 effective surface coverage curves need to be acquired.This system of equations can be solved by first assigning the nominalsurface coverages c_(n) m_(n), y_(n) and k_(n) to the correspondingeffective surface coverages c, m, y and k and then by performing severaliterations, typically 5 iterations, until the system converges.

This reduction in the number of surface coverage curves andsimplification of the ink spreading equations will be published on the29^(th) of Jan. 2008 in a paper by T. Bugnon, R. D. Hersch, Simplifiedink spreading equations for CMYK prints, in SPIE Vol. 6807.

Scalar Initial Thicknesses

The accurate computation of ink thickness variations requires anexplicit expression of ink transmittances. Transmittances may be deducedfrom measured reflectances with any spectral prediction model, in whichthe ink transmittances are explicitly expressed.

In most printing processes, there is trapping, i.e. the respective inkthicknesses of superposed inks are modified (generally reduced). Thedisclosed ink thickness variation computation model takes care oftrapping by computing the internal transmittances t_(ij) of colorantsobtained by the superposition of two inks, of three inks t_(ijk) and offour inks t_(ijkl) from the internal transmittance of the individualinks t_(c), t_(m), t_(y), t_(k) and from their respective fitted reducedthicknesses. For each superposition of solid inks we compute theirrespective thicknesses, called “initial thicknesses”.

For each solid ink contributing to a superposition of solid inks, called“solid colorant”, each solid ink wavelength-dependent spectraltransmittance has an initial scalar thickness. Since we performcomputations with relative thickness values, the initial thickness of asingle ink is one. For two superposed inks i and j, two initialthicknesses d_(Ij) and d_(iJ) for the inks i and j respectively arefitted, by starting from a unit thickness. The same applies for 3 inksor for 4 inks. In Eqs. (9) below, for example, the initial thicknessd_(iJk) expresses the initial thickness of ink j, when superposed withinks i and k. The initial thickness d_(ijK) expresses the initialthickness of ink k, when superposed with inks i and j. Similardenominations apply for the other initial thicknesses.t(λ)_(ij) ={circumflex over (t)} _(i)(λ)^(d) ^(Ij) *{circumflex over(t)} _(j)(λ)^(d) _(iJ)t(λ)_(ijk) ={circumflex over (t)} _(i)(λ)^(d) ^(Ijk) *{circumflex over(t)} _(j)(λ)^(d) ^(iJk) *{circumflex over (t)} _(k)(λ)^(d) ^(ijK)t(λ)_(ijkl) ={circumflex over (t)} _(i)(λ)^(d) ^(Ijkl) *{circumflex over(t)} _(j)(λ)^(d) ^(iJkl) *{circumflex over (t)} _(k)(λ)^(d) ^(ijKl)*{circumflex over (t)} _(l)(λ)^(d) ^(ijkL)   Equations (9)where {circumflex over (t)}_(i)(λ),{circumflex over(t)}_(j)(λ),{circumflex over (t)}_(k)(λ),{circumflex over (t)}_(l)(λ)are respectively the initially computed wavelength-dependenttransmittances of single solid inks i, j, k, l of the calibrationpatches, calculated according to Eq. (6). By inserting the coloranttransmittances t(λ)_(ij), t(λ)_(ijk), t(λ)_(iklj) of Eqs. (8) for allink superposition conditions into Eq. (1a), or respectively (1b), theunderlying spectral prediction model becomes an ink thickness enhancedspectral prediction model.

Ink Thickness Variation Factors

The introduction of ink thickness variation factors within the spectralprediction model allows the deduction of ink thickness variations fromspectral light reflectance, respectively the multi-channel lightreflectance sensor response of halftones. Such halftones are generallypresent at specific locations within a printed page (e.g. within areproduced color image). We introduce the ink thickness variations intoEqs. (9) by multiplying each initial ink thickness with a scalar inkthickness variation factor (also simply called “ink thicknessvariation”). There is one ink thickness variation factor percontributing ink and it does not depend on the superposition condition,i.e. with which other ink (or inks) the considered ink is superposed.The transmittances of single ink, two ink, three ink and four ink solidcolorants are expressed by ink transmittances (symbol: {circumflex over(t)}) initial ink thicknesses (symbol: d) and ink thickness variationfactors (symbol: dr), see Eqs. (10).t(λ) _(i) ={circumflex over (t)} _(i)(λ)^(dr) ^(i)t(λ)_(ij) ={circumflex over (t)} _(i)(λ)^(d) ^(Ij) *^(dr) ^(i)*{circumflex over (t)} _(j)(λ)^(d) ^(iJ) *^(dr) ^(j)t(λ)_(ijk) ={circumflex over (t)} _(i)(λ)^(d) ^(ijk) *^(dr) ^(i)*{circumflex over (t)} _(j)(λ)^(d) ^(iJk) *^(dr) ^(j) *{circumflex over(t)} _(k)(λ)^(d) ^(ijK) *^(dr) ^(k)t(λ)_(ijkl)={circumflex over (t)}_(i)(λ)^(d) ^(Ijkl) *^(dr) ^(i)*{circumflex over (t)} _(j)(λ)^(d) ^(iJkl) *^(dr) ^(j) *{circumflex over(t)} _(k)(λ)^(d) ^(ijKl) *^(dr) ^(k) *{circumflex over (t)} _(l)(λ)^(d)^(ijkL) *^(dr) ^(l)   Equations (10)where the thickness variation factor of ink i is dr_(i), of ink j isdr_(j), of ink k is dr_(k) and of ink l is dr_(l).

In the case of cyan, magenta, yellow and black inks, we express the 16colorant transmittances as follows.t_(C)={circumflex over (t)}_(C) ^(dr) ^(C) ; transmittance of solidcolorant cyant_(M)={circumflex over (t)}_(M) ^(dr) ^(M) ; transmittance of solidcolorant magentat_(Y)={circumflex over (t)}_(Y) ^(dr) ^(Y) ; transmittance of solidcolorant yellowt_(K)={circumflex over (t)}_(T) ^(dr) ^(K) ; transmittance of solidcolorant blackt _(CM) ={circumflex over (t)} _(C) ^(d) ^(Cm) *^(dr) ^(C) *{circumflexover (t)} _(M) ^(d) ^(cM) *^(dr) ^(M) ; transmittance of solid colorantcyan+magenta (blue)t _(CY) ={circumflex over (t)} _(C) ^(d) ^(Cm) *^(dr) ^(C) *{circumflexover (t)} _(Y) ^(d) ^(cY) *^(dr) ^(Y) ; transmittance of solid colorantcyan+yellow (green)t _(CK) ={circumflex over (t)} _(C) ^(d) ^(Cm) *^(dr) ^(C) *{circumflexover (t)} _(K) ^(d) ^(cK) *^(dr) ^(K) ; transmittance of solid colorantcyan+blackt _(MY) ={circumflex over (t)} _(M) ^(d) ^(My) *^(dr) ^(M) *{circumflexover (t)} _(Y) ^(d) ^(mY) *^(dr) ^(Y) ; transmittance of solid colorantmagenta+yellow (red)t _(MK) ={circumflex over (t)} _(M) ^(d) ^(Mk) *^(dr) ^(M) *{circumflexover (t)} _(K) ^(d) ^(mK) *^(dr) ^(K) ; transmittance of solid colorantmagenta+blackt _(YK) ={circumflex over (t)} _(Y) ^(d) ^(Mk) *^(dr) ^(Y) *{circumflexover (t)} _(K) ^(d) ^(yK) *^(dr) ^(K) ; transmittance of solid colorantyellow+blackt _(CMY) ={circumflex over (t)} _(C) ^(d) ^(Cmy) *^(dr) ^(C)*{circumflex over (t)} _(M) ^(d) ^(cMy) *^(dr) ^(M) *{circumflex over(t)} _(Y) ^(d) ^(cmY) *^(dr) ^(Y) ; transmittance of cyan+magenta+yellowt _(MYK) ={circumflex over (t)} _(M) ^(d) ^(Myk) *^(dr) ^(M)*{circumflex over (t)} _(Y) ^(d) ^(mYk) *^(dr) ^(Y) *{circumflex over(t)} _(K) ^(d) ^(myK) *^(dr) ^(K) ; transmittance ofmagenta+yellow+blackt _(CYK) ={circumflex over (t)} _(C) ^(d) ^(Cyk) *^(dr) ^(C)*{circumflex over (t)} _(Y) ^(d) ^(cYk) *^(dr) ^(Y) *{circumflex over(t)} _(K) ^(d) ^(cyK) *^(dr) ^(K) ; transmittance of cyan+yellow+blackt _(CMK) ={circumflex over (t)} _(C) ^(d) ^(Cmk) *^(dr) ^(C)*{circumflex over (t)} _(M) ^(d) ^(cMk) *^(dr) ^(M) *{circumflex over(t)} _(K) ^(d) ^(cmK) *^(dr) ^(K) ; transmittance of cyan+magenta+blackt _(CMYK) ={circumflex over (t)} _(C) ^(d) ^(Cmyk) *^(dr) ^(C)*{circumflex over (t)} _(M) ^(d) ^(cMyk) *^(dr) ^(M) *{circumflex over(t)} _(Y) ^(d) ^(cmYk) *^(dr) ^(Y) *{circumflex over (t)} _(K) ^(d)^(cmyK) *^(dr) ^(K) ; transmittance of cyan+magenta+yellow+blackt_(W)={circumflex over (t)}_(W); transmittance of unprinted paper, bydefinition equal to 1 at all wavelengths.  Equations (11)

In the solid colorant transmittances above (Eqs. 11), the superpositiondependent initial thicknesses are calibrated during the calibrationphase according to equations (9). At printing time, the ink thicknessvariation factors are the fitted unknowns. For cmyk inks, the thicknessvariation factors of cyan, magenta, yellow and black are respectivelydr_(C), dr_(M), dr_(Y) and dr_(K). The ink thickness variationcomputation model now consists of Eqs. (1a) or (1b, 1c), and (3) inwhich transmittances t₁ to t₁₆ are expressed by the 16 transmittancespresent in Eqs. (11), which in the case of 4 inks are a function of the4 ink thickness variation factors.

The spectral ink thickness variation computation model enables obtainingthe ink thickness variations of a printing system (a) on speciallydefined test patches, (b) on freely chosen print image locations and (c)with sensor responses over an area segment (i.e. along a thin rectangleof a short length, e.g. 1 mm×2 mm or 2 mm×2 mm) within the printedsheet. Only nominal surface coverages, as defined by the prepresssystem, need to be known. Accurate ink thickness variation factors canbe fitted thanks to the ink thickness variation computation model oncethe initial ink thicknesses are fitted and the effective coverage curveshave been established (either during offline initial calibration orduring online calibration). With the effective surface coverage curves,nominal surface coverages of inks are mapped into effective surfacecoverages of inks, from which the effective surface coverages a_(j) ofthe colorants are computed according to the Demichel equations (4) andinserted into respectively Eq. (1a) or Eq. (1b).

As an example, FIG. 1 shows a diagram of the ink thickness variationcomputation model for the three inks cyan, magenta and yellow. Itcomprises respectively the input nominal surface coverages of c, m, andy 101, the operation 102 of weighting the surface coverages curves 112according to the surface coverages of the underlying colorants in orderto obtain the effective surface coverages c′, m′, and y′ 105, thecomputation 103 of the effective colorant coverages according to theDemichel equations, the ink thickness and sensor response extendedspectral prediction model 104, which receives as input 109 measuredsensor responses (e.g. q_(r), q_(g), q_(b)) or sensor density responses.Initially calibrated parameters comprise the ink transmittances 106, andthe initial ink thicknesses 107 for each ink in each possible inksuperposition (colorant). Parameters calibrated or recalibrated at thebeginning of the print session comprise the paper or substratereflectance r_(g) 108 and possibly the effective coverage curves foreach useful superposition condition 113. The output of the model are thecyan, magenta, and yellow ink thickness variation factors 110 dr_(C),dr_(M), and dr_(Y). In FIG. 1, the initial thicknesses 107 are labeledd_(i) for the initial thickness of a single ink, d_(Ij) for the initialthickness of one ink i superposed with another ink j, and d_(Ijk) forthe initial thickness of one ink i superposed with two other inks j andk. Ink layers I, j, and k are different one from another and areplaceholders for every of the 3 possible inks of the considered printingsystem.

FIG. 2 is a generalization of the ink thickness variation computationmodel shown in FIG. 1, for a freely chosen set of four different inksI₁, I₂, I₃, I₄ of surface coverages c₁, c₂, c₃, c₄ (201). Box 211represents the connections between input nominal ink surface coverages201 and their corresponding mappings 212 to effective surface coveragesf_(i)(i), f_(i/j)(i), f_(i/jk)(i), f_(i/jkl)(i) in the differentsuperposition conditions i alone, i superposed with j, i superposed withj and k, and i superposed with j, k and l, where i,j, k and l areplaceholders for any of the inks and are different one from another.Surface coverages 213 are weighted 202 according to the underlyingcolorants to yield after a few iterations the effective surfacecoverages c₁′, c₂′, c₃′, c₄′ (205). Thanks to the colorant computationequations 203 (Demichel in case of independently printed ink layers,Eqs, (4)), one obtains the effective surface coverages a₁′, to a₁₆′(214). The ink thickness variation extended spectral prediction model204 fits the ink thickness variations 210 dr₁ of ink I₁, dr₂ of ink I₂,dr₃ of ink I₃ and dr₄ of ink I₄ by minimizing a difference metricbetween predicted sensor responses and measured sensor responses 209q_(α), q_(β), q_(γ), q_(δ) or possibly by minimizing the sum of suchdifferences for several measurements performed at different locations ofthe printed sheet. Parameters deduced either from initial offline orfrom online calibration comprise the ink transmittances 206, the initialink thicknesses 207 for each ink superposed with any other combinationof inks (different colorants) and the paper reflectance 208 (R_(g)). Onepossible embodiment of the ink thickness variation computation model ofFIG. 2 is a printing system printing with cyan, magenta, yellow andblack inks.

The ink thickness variation computation model shown in FIG. 2 can beextended in several ways.

(A): Instead of having 4 sensors with spectral sensibilities indifferent parts of the considered wavelength range (visible and nearinfra-red), one may introduce 5, 6 or more sensors.

(B): Since some printing systems employ more than 4 inks (examples ofpossible additional inks: orange, dark blue, light cyan, light magenta,etc.), the ink thickness variation computation model can becorrespondingly extended by introducing as many nominal 201 andeffective 205 ink surface coverages as inks, as many transmittances 206as inks, as many effective surface coverage curves 212 and initial inkthicknesses 207 as used superpositions of inks and as many ink thicknessvariations 214 as inks.

Calibration of the Ink Thickness Variation Computation Model

We distinguish between an off-line initial calibration for a given classof printers, papers and inks and an optional online calibration (orrecalibration) for further tuning the calibration according to thecurrent printing conditions (current paper, currently used set of inks,current temperature, etc.). The off-line calibration may be performedonce (e.g. in the factory) by the manufacturer of the printer,respectively printing press, and delivered or made available fordownload as a computer file, called “initial calibration data”.

The initial calibration of the ink thickness variation computation modelcomprises the deduction of the transmittances of the inks and possiblyan initial set of effective surface coverage curves. During the initialcalibration, the spectral reflectances of unprinted paper and of allsolid ink and solid ink superpositions are measured by a spectralmeasurement device. The Clapper-Yule internal reflectance of paperr_(g)(λ) is deduced by equation (5). Ink and colorant transmittances arededuced according to Eq. (6) or respectively according to Eq. (1c). For4 inks (e.g. cmyk), 16 spectral measurements are needed. Initialthicknesses are fitted according to equations (9), by minimizing adistance metric between predicted colorant transmittance spectra andtransmittance spectra deduced from colorant measurements.

Initial surface coverage curves can be obtained for the relevantsuperposition conditions by measuring single halftone patches (e.g. at50% nominal surface coverages), deducing the corresponding effectivesurface coverages and creating the effective surface coverages curves byinterpolation. According to Equations (8), for creating 20 surfacecoverage curves, one needs 60 measurements in the case of 3 differentsurface coverages per curve or 20 measurements in the case of a singlesurface coverage measurement per curve. For deducing effective surfacecoverages during the initial calibration, one may measure halftonereflectance spectra and fit the effective surface coverages byminimizing a distance metric between reflection spectra predictedaccording to Equation (1a) or (1b) and measured reflection spectra.Alternately, for example during online calibration, one may measure thesensor responses q_(α), q_(β), q_(γ), q₆₇ and, according to Equations(1a) or (1b) and (3), fit the surface coverages by minimizing a distancemetric between predicted and measured sensor responses.

The online calibration (when applicable also called recalibration) ofthe paper reflectance (from which in the case of the CYSN model theinternal paper reflectance is derived) and of the surface coveragecurves is performed on the running printer or press, once the printsmatch the desired quality. The recalibration of the paper reflectanceR_(g)(λ) according to the current print sheet paper is performed byreplacing the paper reflectance R_(g)′(λ) measured during the initialcalibration by a scaled paper reflectance R_(g)(λ)=R_(g)′(λ)s_(g)+o_(g),where s_(g) is a scaling factor and o_(g) is an offset, both fitted byminimizing a difference metric between sensor responses predictedaccording to Eq. (3) for white paper and corresponding measured sensorresponses. To reduce the impact of noise, it is preferable to minimizethe sum of such difference metrics for several paper locations.

The online calibration (or recalibration) of the effective surfacecoverage curves is performed as follows. Sensor response predictions fora number of area segments are made on the running press, by consideringthe effective surface coverage curves as free variables and by fittingthese effective surface coverage curves so as to minimize the sum of adifference metric between measured sensor responses and predicted sensorresponses at different printed sheet locations. A surface coverage curvemay be given as a corresponding dot gain curve, where dot gain isdefined as the effective surface coverage minus the nominal surfacecoverage. The dot gain curve may be given by a single quadratic Bézierspline through the points (0,0), (0.5, dot gain at 50%), (1,0). In apreferred implementation, this dot gain curve, and therefore thecorresponding surface coverage curve are fitted by fitting the dot gainat 50% surface coverage.

Layout of Illuminating and Sensing Devices

Since there may be variations of ink thicknesses across the printedsheet, compact elements comprising the illuminating and sensing devices(FIG. 3, 308) may be repeated along the width 321 of the printed sheet301, or in the case of a printing press, at the location of each inkzone. These elements are positioned on the path way of the printedpaper. In a preferred embodiment (FIG. 5A), each sensor of a 4-channelsensor device may have its own illumination, either white lightincluding infra-red components or light formed by a light emitting diode(LED) emitting within a given spectral wavelength range. In a possibleembodiment, the light 505 is guided by a waveguide 503 (or by an opticalfiber) to hit the print surface 501 at an angle of approximately 45degrees. In the case of white light, a corresponding red, green, blue orinfra-red filter 509 is placed in the light path of the light, e.g. atthe entry of the waveguide. Optionally, the waveguide for the incidentlight may be terminated by a lens (possibly Fresnel lenses) 506 whichfocus the light onto the print surface. In alternative embodiments, thefilters may be integrated into the lens by diffusing a partiallyabsorbing layer at its surface or by creating the lens with a partiallyabsorbing substance. In a further alternative, the waveguide may also beconceived to filter light at a given wavelength range.

To avoid capturing specular reflections, the reflected light is capturedperpendicularly to the print surface, e.g. by being focused by a lens507 in front of an optional waveguide 508. The sensor 504 may either bedirectly in front of the print, or hooked onto the waveguide 508transmitting the light which is perpendicularly reflected from the printsurface. The sensor 504 is generally an integrated circuit bonded ontoan electronic circuit board 502.

A compact embodiment (FIG. 5B) may comprise a light source embodied by aLED 513 emitting in the blue, green, red or respectively in thenear-infra-red wavelength range, a polarizing filter 514 polarizing theincident light according to a given orientation, a waveguide 515 guidingthe light to a beam splitter 510 which directs the incoming polarizedlight perpendicularly into the print surface 517. The part of incidentpolarized light specularly reflected at the surface of the print isdiscarded by a second polarization filter 511 located on the reflectedlight path. This output polarization filter is rotated by 90 degrees inrespect to the input polarization filter 514, located within theincident light path. Light crossing the print interface 517 istransmitted onto the print substrate (e.g. paper), is scattered withinthe substrate and becomes depolarized. It is reflected by the substrate,reaches the light guide, possibly through a focusing lens, traverses thebeam splitter in the reverse direction, traverses the polarizationfilter 511 and strikes the sensor 512, in the present embodiment, theSPAD (see next section). The two polarizing filters discard specularreflections, which may be high when the ink is still wet on the printedsheet. Many different variants equivalent to the present embodiment maybe considered, such as using white light filtered by the inputpolarization filter and further filtered by blue, green, red orinfra-red filters instead of a LED followed by the input polarizationfilter. As previously, the sensor 512 is an integrated circuit locatedon a printed circuit board 518 and the LED 513 is also connected 519 tothe printed circuit board.

In a further embodiment (FIG. 5C), the white light source 534 may have acertain length and illuminates the print sheet parallel to the paper(537) moving orientation, along the multi-channel sensing devices (530,531, 532, 533). Alternately, the elongated white light source may bepositioned over the full length of the printed sheet width and createthe illumination for many or all sensing devices. In both cases, eachsensing device may comprise a coating 530 with a filtering substance onthe focalizing lens 531. An optional waveguide 532 connects the lens tothe sensor 533. These elements can be fixed on a printed circuit board538.

Each of the 4 illuminating/sensor devices (FIGS. 3 and 4A, 304, 305,306, 307) may be placed at successive positions within the path of themoving paper. For example, by placing them one or several millimetersapart one from another, reflected light captured by one sensor devicedoes not contribute to the light captured by its neighbor device.

In order to capture ink thickness variations across the full sheetwidth, 4-channel illuminating/sensor sets 308 may be placed at regularintervals across the paper width, perpendicularly to the paperdisplacement orientation. In the case of offset presses, it is advisableto place at least one set of 4-channel illuminating/sensor deviceswithin each ink zone.

Processing of the Sensor Outputs

In the considered embodiment, the electronic signal (FIG. 4A, 401, 402,403, 404) emitted by each of the 4 sensors according to the illuminationand the reflectance of the underlying sensed area of the printed sheetdepends on the sensor technology. The preferred technology is the SinglePhoton Avalanche Diode (SPAD), see S. Cova, et. al., Avalanchephotodiodes and quenching circuits for single-photon detection, AppliedOptics, Vol. 35, Issue 12, pp. 1956-1976 (April 1996) as well as E.Charbon, Techniques for CMOS Single Photon Imaging and Processing,6^(th) Intl. Conf. on ASIC, IEEE ASICON 2005, pp. 1163-1168, referencedas [Charbon05], hereby incorporated by reference. Other technologies,such as Charged Coupled Devices (CCDs), or CMOS may also be used assensors. The advantage of SPADs is their ability of counting singlephoton events, i.e. the possibility of very short sensor responseacquisition times, between hundreds of nanoseconds to a few millisecondsand to provide a high signal to noise ratio, and therefore a higheffective dynamic range.

A set of multi-channel sensors may also be integrated within a singleintegrated circuit (FIG. 4B, 440). In the embodiment of FIG. 4B, aquadruplet of SPAD sensors 414, 415, 416, 417 comprise their own pulsecounters 424, 425, 426, 427 and counter output lines 434, 435, 436, 437.The counter output lines may be multiplexed by an internal multiplexer438, whose output is connected for example via a communication bus 460to the sensing system microcontroller 470. Such integrated multi-channelsensors may be replicated over the width of the print sheet. An exampleis the replicated multi-sensor integrated circuit 450, also connected tothe sensing system microcontroller 470 through the communication bus460.

In the case of paper printed at a speed of for example 2 meter persecond (m/s), a sensor response acquisition time (also called sensoractive time or sensor aperture time) of one. millisecond, counting thephotons captured by the SPAD during 1 ms, corresponds to a displacementof the paper by 2 mm, i.e. a sensed area segment length of 2 mm. Withina printed sheet, many area segments of this size have a nearly uniformcolor, i.e. are composed of color pixels varying one in respect to another by less than CIELAB ΔE₉₄=6.

At a speed of 10 m/s, the sensed area segment length is 10 mm. Within aprinted sheet either a close to uniform color area segment of that sizecan be located within the printed sheet and in the region of interest(e.g. an ink zone), or a non uniform area segment is selected, andsubdivided into parts. For predicting its multi-channel sensor response,the multi-channel response of each part is separately predicted. Thepredicted multi-channel sensor response for the whole area segment isthe weighted average of the separately predicted parts, the weightscorresponding to the respective relative surfaces of these parts.

In the preferred SPAD embodiment, the sensing devices are connected to asensor processing module (FIGS. 3A and 3B, 320) which comprises amultiplexer 310, a counter 311, fast logic (FL) 312 and amicrocontroller (μC) 316. The signal lines 309 arriving from theindividual SPAD sensors transmit serially the pulses corresponding tophoton counts to a multiplexer (FIG. 3B, 310), which selects the sensorwhich must be currently read out. The output of the multiplexer 314 isforwarded to the counter (CTR) 311 which is enabled 316 by the fastlogic 312 to count the pulses during the desired active time of theSPAD, i.e. during the passage of a desired paper area segment beneaththe corresponding sensor. The output of the counter 315 giving thesensor response in term of intensity is stored in the sensing systemmicrocontroller 313 responsible for the control of the present sensingsystem. The sensor devices 308 as well as the elements of the sensorprocessing module 320 may be attached to a same printed circuit board303.

The sensing processing module microcontroller 313 connected to the maincomputing system (FIG. 7, 701) by a communication link 317 (FIGS. 3A and3B), e.g. USB (Universal Serial Bus), receives from the main computingsystem timing information about the location of the area segments whosesensor responses need to be read out. The sensing processing modulemicrocomputer communicates 324 with the fast logic 312, for exampleembodied by a field programmable gate array (FPGA), and initializes itto create the signals 318 (FIGS. 3A, 3B and 4A) driving the sensorenabling inputs, the signals driving the multiplexor 319, and thesignals resetting 325 and enabling 316 the counter 311. The sensingprocessing module microcontroller 313 transmits the sensor responses tothe main computer. Thanks to the sensor responses, the main computingsystem (FIG. 7, 701) computes the ink thickness variations, and ifnecessary, applies corresponding corrections to the printer actuationvariables such as the amount of deposited ink. For a printing press,deduction of ink thickness variations enables automatically regulatingthe ink flow by acting on the print actuation parameters such as thefeed of ink.

In the case of sensors embodied by SPADs, one may conceive anilluminating/sensing device where (a) all sensors continuously providepulses according to the incoming photons, (b) the multiplexor 310selects the currently active sensor and the fast logic 312 defines theacquisition time and period by activating the reset signal 325 of thecounter before the acquisition and by activating the counter's countenable signal 316 during the acquisition period (few hundreds ofnanoseconds to a few milliseconds).

According to [Charbon05], the duration of a full photon detection cyclecalled dead time (tD) is between 20 ns and 50 ns, depending on theimplementation of the SPAD. The maximal number of detected photonsduring the sensor active time t_(A), called max photon count (N_(max)),is N_(max)=t_(A)/t_(D). For example, with a sensor active time t_(A) of1 ms, and a dead time of t_(D) of 50 ns, the largest number of detectedphotons is 20,000. The Poisson noise yields a number of pulsesN_(Poisson)≈√{square root over (N_(max))}. Without accounting for thedark count rate which is negligible in the present case (about 300pulses per second, i.e. less than one pulse per millisecond on average),we obtain a signal to noise ratioSNR=20 log(N _(Max)/√{square root over (N_(Max))})=20 log √{square rootover (N_(Max))}  (12)

In the example above, the signal to noise ratio is SNR=20 log √{squareroot over (20000)}=43 dB.

This signal to noise ratio is high since, with an SPAD, pulses aredirectly converted into TTL or CMOS compatible pulses and counted. Thereis no need for an amplifier, a sampler and an A/D converter whichintroduce additional noise. With a maximal signal √{square root over(N_(max))} times higher than the noise, it becomes possible to buildhigh-speed sensors capable of sensing very low reflectances in the rangebetween 1/100 and 1/1000, i.e. corresponding to reflectance densitiesbetween 2 and 3.

The maximal photon count N_(max) defines the size of the counter (FIG.3, 311) in terms of its number of bits. For N_(max)=20000, a 15 bitscounter is sufficient. It is however easy to reach N_(max)=100,000 witha 17 bits counter or N_(max)=1,000,000 with a 24 bits counter.

Spectral Sensibilities of the Sensing System

If the illuminating device is white light, red, green, blue or infra-redfilter is placed within the light path, before the corresponding sensor.In one embodiment, the red, green, and blue filters have similarspectral sensibilities as the sensibilities used for buildingdensitometers, which are specified by DIN standard 16536-2. Theinfra-red sensibilities should cover a part of the near-infra-redspectrum, for example between 730 nm and 900 nm.

FIG. 6 shows the blue (B: 601), green (G: 602) and red (R: 603)normalized sensitivities according to DIN standard 16536-2 used forderiving the densities of the corresponding cyan, magenta and yellow inkpatches. These sensitivities correspond to the multiplication of thesensibilities of filters in front of the sensors and the own sensitivityof the sensors. In a possible embodiment, these sensitivities, togetherwith the near infra-red sensitivity (IR: 604) can be used for thepresently proposed 4 sensor sensing system.

If the illuminating devices are LEDs, then the light of the chosen red,green blue and infra-red LEDs should be directed to the print surface,be reflected and sensed by the corresponding sensor. The sensorsensibilities should be known, and should provide a positive response atthe wavelengths of the blue, green, red and infra-red LEDs, preferablylocated respectively between 380 nm and 480 nm, between 500 nm and 600nm, between 620 and 720 nm and between 750 nm and 900 nm. In the casethat the sensibility of the sensor is not given by the sensormanufacturer, it can be deduced experimentally by irradiating the sensorwith light at narrow wavelengths, e.g. at each 10 nm between 380 nm and900 nm, and by measuring the corresponding responses.

Thickness Variations Deduced from Area Segments within a Printed Sheet

The present invention aims at deducing ink thickness variations at printtime. Since during the print operation the printed paper is movingforward at a given speed, we measure the sensor responses over an areasegment of the print along the paper movement orientation. The positionof the paper in respect to the sensors is known at any time. The sensoracquisition logic may acquire the sensor responses at regular timeintervals. The sensor responses from area segments known to be nearlyuniform are memorized and forwarded to the computing system whichdeduces the ink thickness variations. As an alternative, by interactingwith the microcontroller 313 which drives the sensor acquisition logic(FIG. 3B, 312), the software running on the computing system may launchthe sensor acquisition at a location on the print where the area segmentis nearly uniform.

When acquired from nearly uniform area segments, the sensor responsesintegrated over an area segment are considered to be the sensorresponses of a uniform halftone patch whose nominal surface coveragesare the mean of the nominal surface coverages (e.g. nominal c,m, y, andk values) of the corresponding area segment pixels within the prepresssheet image.

The ink thickness variations, expressed by the ink thickness variationfactors, for the considered area segment are obtained by minimizing adistance metric between the predicted area segment sensor responses andthe measured area segment sensor responses, for example by minimizingthe sum of square differences between the predicted area segment sensordensity responses and the measured area segment sensor densityresponses. Accurate results which reduce the impact of noise areobtained by measuring the sensor responses at several area segmentlocations and by minimizing the sum of these distances between predictedand measured sensor responses at these locations.

In the case of the cyan, magenta, yellow and black inks, in order tocreate for each ink an independent absorption wavelength range, weconsider wavelengths incorporating both the visible wavelength range(380 nm to 730 nm) and the near-infra-red wavelength range (e.g. 740 nmto 900 nm). In the near-infra-red wavelength range, the cyan, magentaand yellow colorants do not absorb light. Only the pigmented black inkabsorbs light. An ink thickness variation model with a wavelength rangefrom 380 nm to 900 nm, i.e. with the visible and near-infra-redwavelength ranges, enables computing ink thickness variations for thecyan, magenta, yellow and black inks. FIG. 2 gives a schematic view ofthe ink thickness variation computation system, for 4 inks I₁, I₂, I₃,and I₄, which may represent the cyan, magenta, yellow and black inks.

Normalized Ink Thickness Variation Computation

In the case of small variations between the calibration and the printeroperating conditions (e.g. the ink density during calibration differsslightly from the ink density during normal printing operation) moreaccurate results may be obtained by computing normalized ink thicknessvariations.

Normalized ink thickness variation computation requires establishingreference ink thickness variations dr₁′, dr₂′, dr₃ 40 , dr₄′ (FIG. 2,214) on a reference print under reference settings of the printingdevice. In order to create the reference settings, the printed colorpictures are observed and verified (e.g. compared with a soft proof on acalibrated display) by a print operator. Alternately, it may be possibleto use another print verification system (see “Background of theinvention”). As soon as the current print result meets the desiredquality criteria (e.g. a color picture close to the desired colorpicture or ink densities within a given tolerance range), the referenceink thickness variations are deduced by measuring the area segmentsensor responses at different area segment locations, by predicting thearea segment sensor responses at these locations, by deriving at eachlocation according to a difference metric the distance between measuredand predicted area segment sensor responses and by fitting the inkthickness variations so as to minimize the sum of the computed distancesacross the considered area segment locations. The fact that severalcolor area segments contribute to the computation of the reference inkthickness variations reduces the impact of noise present within theindividual area segments.

From now on, ink thickness variation computations are normalized inrespect to these recorded reference thickness variations dr₁′, dr₂′,dr₃′, dr₄′, i.e. the ink thickness variation computing system computesthe normalized ink thickness variations dr₁, dr₂, dr₃, dr₄ in respect tothe initial ink thicknesses multiplied by the corresponding referenceink thickness variations. FIG. 8A illustrates normalized ink thicknessvariations 804 (axis 801) deduced from polychromatic halftones presentin printed sheets of the magenta ink 801, and of the black ink (FIG. 8B,814, axis 811) for many different print trials, where the ink feed ofone or of several inks has been increased or decreased. In FIGS. 8A and8B, print trials 802 are characterized by a variation of the amount ofdeposited ink. C+, M+, Y+, K+ indicate respectively a higher ink feed ofthe cyan, magenta, yellow and black inks and C−, M−, Y−, K− indicaterespectively a lower ink feed of the cyan, magenta, yellow and blackinks. The labels “+”, “−”, “0” indicate respectively an increment, adecrement or a constant value of the ink feed for the considered ink(FIG. 8A: magenta ink, FIG. 8B: black ink). In order to provide acomparison with the real amount of deposited ink, the black triangles,placed according to the vertical axis on the right of FIGS. 8A (803) and8B (813), indicate the corresponding measured relative scalar densityvalues, i.e. the solid ink density values measured on special patcheslocated on the trial print sheet divided by the solid ink density valuesmeasured on the reference print sheet without any ink feed increase ordecrease. The reference print trial is located at the leftmost position.The gray bars in FIGS. 8A and 8B indicate the range of values where nosignificant ink thickness variations occur.

Ink Thickness Variation Computation in Respect to Reference Settings

In a further embodiment, the system may track ink thickness variationsat print time without knowing the nominal surface coverages of inks, butafter having performed reference settings of the print controlparameters of the printing press (e.g. ink feed) by an operator and/orby another print calibration system. Under the reference settings,sensor responses (e.g. q_(α)′, q_(β)′, q_(γ)′, q_(δ)′, FIG. 2, 215) aremeasured from within specific area segments of a printed sheet. Then,ink thickness variations occurring when printing that sheet can bededuced by the ink thickness variation computing system.

The reference effective surface coverages and possibly referencethickness variations are deduced from the reference sensor responses andrecorded. Then, while printing the same print sheet, or when printingthe same print sheet again in a new print session, the correspondingsensor responses are measured. The ink thickness variation computingsystem then computes the ink thickness variations occurring in respectto the reference settings. In the present embodiment, the ink thicknessvariation computing system does not depend on the knowledge of nominalsurface coverages. It depends only on the initial calibration of inktransmittances, of initial ink thicknesses and on the measured sensorresponses. Since only the effective surface coverages are used,calibration is simplified by avoiding the need to establish theeffective surface coverage curves.

Ink Thickness Variation Computation

The method for computing ink thickness variations comprises the step ofcalibration of a thickness variation and sensor response enhancedspectral prediction model by (a) measuring the paper reflectance, ifapplicable, deducing the internal paper reflectance and deducingspectral ink transmittances from spectral measurements, (b) computingthe scalar ink thicknesses of the superposed inks forming a solidcolorant and (c) computing the effective coverage curves for halftonesin different superposition conditions. Steps (b) and (c) can beperformed either by spectral measurements of by sensor responses.

In order to adapt an initial calibration to the current print conditions(state of the printer, temperature, paper, inks), the ink thicknessvariation computation method also comprises the optional step ofrecalibrating at printing time the paper reflectance and the effectivesurface coverage curves.

It further comprises the step of fitting, during print operation,according to the thickness variation and sensor response enhancedspectral prediction model, for each contributing ink, the correspondingink thickness variation factors. This is performed by minimizing adistance metric such as the sum of square differences between thepredicted sensor responses and the measured sensor responses. In thecase of cyan, magenta, yellow and black inks, the presently disclosedink thickness variation computation method works simultaneously withinthe visible and the near-infra-red wavelength range domain.

In order to even better adapt the initial calibration to the currentprint conditions (state of the printer, temperature, paper, inks), anoptional reference thickness variation computation step enablescomputing reference thickness variations which are used for computingnormalized ink thickness variations during print operation.

A further ink thickness variation computation method variant alsocomprises, during online calibration, the step of measuring referencesensor responses from specific locations of the print, of deducingcorresponding reference effective surface coverages and of computing inkthickness variations by minimizing a distance metric between the sensorresponses predicted according to the thickness variation enhancedspectral prediction model and the measured sensor responses. This methoddoes not need as calibration data the effective surface coverage curves,but relies on the reference sensor responses recorded under referencesettings to compute the reference effective surface coverages (seesection “Ink thickness variation computation in respect to referencesettings”).

Ink Thickness Variation Computing System

An ink thickness variation computing system is shown in FIG. 7, 710. Itcomprises a computing system 701 and a sensing system 708. The sensingsystem is made of an array 702 of illuminating 703 and sensor devices704 located on the pathway of the printed paper and of a processingmodule 706 for selecting, computing, storing and delivering the sensorresponses to the computing system 701. The processing module receivesfrom a subset of the lines 705 the output of the sensor devices andoptionally transmits through another subset of the lines 705 sensoracquisition synchronization signals. The sensing system's processingmodule 706 is connected to the computing system 701 by a digital link707, for example an USB link.

According to the sensor responses, the computing system 701 computes theink thickness variations by performing the steps described in section“ink thickness variation computation”. The computing system can alsoperform the online calibration or recalibration step of adapting thepaper reflectance and the surface coverage curves (see Section“Calibration of the ink thickness variation computation model”)according to the sensor responses.

When connected to a print actuation parameter driving module 709, theink thickness variation computing system 710 becomes an online printparameter regulation system which regulates actuation parameters such asthe ink feed or the volume of deposited toner per unit of time accordingto the current ink thickness variations.

Specific Advantages of the Present Disclosure

Specific advantageous features of the presently disclosed methods andsystems are:

1. The internal use of a spectral prediction model incorporatingexplicitly ink thickness variations but without the need of expensiveonline spectral reflectance measuring devices. The only requiredspectral measurements are off-line one-time initial calibrationmeasurements for obtaining the paper reflectance and the inktransmittances for a class of similar papers and inks. This can beperformed in the factory manufacturing the printing device. During theprint sessions, the only online measurements are the sensor responses(or equivalently, the sensor density responses), performed withnon-expensive solid-state sensor devices.

2. The multi-channel sensor devices, for example 4 sensor devices, arepreferably embodied by Single Photon Avalanche Diodes (SPADs). Theyallow building high-speed acquisition sensors with a short active time(also called aperture time), typically between a few hundreds ofnanoseconds to a few milliseconds. They induce only very low noise andrequire only simple digital electronics for accumulating and countingthe photon pulses in order to obtain the reflected intensity.

3. Due to the low price of the illuminating/sensor devices,multi-channel sensors can be replicated over the width of the printedsheet, allowing the acquisition of accurate ink thickness informationwithin the full printed sheet. In addition, their low price enablesusing them within cheap mass product printers, such as low cost ink-jet,dye-diffusion, thermal transfer and electro-photographic printers, forthe automatic regulation of print activation parameters. Furthermore,since the presently disclosed sensing system does not require any movingpart, it is also cheap for maintenance.

4. Due to the short sensor acquisition times, in the order of hundredsof nanoseconds to a few milliseconds, sensor responses from short areasegments (length: e.g. one to ten millimeters) can be acquired, whichincorporate a color halftone and no paper white. This avoids therelatively important noise present in the paper white reflectance andprovides more robust results than accounting for color variations withinlong stripe parts (long thin lines along the length of the sheet) asproposed by U.S. Pat. No. 7,252,360 to Hersch et. al.

5. In the present disclosure, we use the ink thickness and sensorresponse enhanced spectral prediction model within a single continuouswavelength range covering both the visible and the near infra-redwavelength range. There is no need for two separate applications of themodel, one in the visible wavelength range and one in the near infra-redwavelength range, as taught by U.S. Pat. No. 7,252,360 to Hersch et. al.By operating over the visible and near infra-red wavelength range, thesensor-based thickness variation computation system can unambiguouslycompute simultaneous thickness variations of the cyan, magenta, yellowand black inks.

6. The effective surface coverage curves expressing the functionsmapping nominal surface coverages into effective surface coverages inthe different superposition conditions, combined with the spectralprediction model incorporating explicit transmittances for all solidinks and with the formula modeling the sensor responses from reflectionspectra and from illuminating device spectra (Equations 3) provideaccurate sensor response predictions.

7. The calibration effort can be reduced in the case of cyan, magenta,yellow and black inks by considering that the superposition of an inkhalftone and solid black yields black and therefore does not have adirect impact on the mapping between nominal and effective surfacecoverage of that ink halftone. This allows reducing the number of curvesmapping nominal to effective surface coverages from 32 to 20.

8. The ink thickness variation prediction model provides improvedthickness variation predictions thanks to the introduction of anoptional online refined calibration of the paper reflectance and of theeffective surface coverage curves performed during print operation(running printer or printing press). The online calibration is performedwith multi-sensor responses on halftones located within normal printeddocument pages.

9. More accurate ink thickness variations are obtained by measuring thesensor responses at several area segment locations and by minimizing thesum of the differences (according to a difference metric) betweenpredicted and measured sensor responses at these locations.

10. When predicting ink thickness variations, we assume that a smallincrease in the amount of ink does not change the ink surface coverages.Therefore, fitting ink thickness variations from sensor responses is thesame as fitting ink volume variations. However, in some printers, anincreased ink thickness also yields an increase of the correspondingeffective surface coverages. Under these conditions, with the methodsdescribed in the present disclosure, we fit ink volume variationsinstead of ink thickness variations. We may consider the deduced inkvolume variations as a multiplication of a pure ink surface variationfactor and a pure ink thickness variation factor. If we want to obtainthe pure ink thickness variation factor we may apply a function to theink volume variation factor, for example a square root function. But inthe general case, we can use directly the deduced ink volume variationsto regulate the print actuation parameters such as the ink feed.

General Advantages

In addition to the specific advantages described above, the inventionhas also similar advantages as taught by U.S. Pat. No. 7,252,360 toHersch et. al.:

1. The ink thickness variations which have been introduced into thespectral prediction model are exactly the variables needed to controlthe ink deposition process within a printing press or a printer.

2. The fact that ink thickness variations of the contributing inks canbe computed from sensor measurements at various locations within theprinted document pages enables avoiding printing special patches orcontrol strips at the border of the printed sheet and therefore alsoavoids the need to cut these elements out after printing.

3. In case that the calibration conditions deviate slightly from thenormal print operating conditions, a recorded set of reference inkthickness variations enables deducing during print operation normalizedink thickness variations with an improved precision.

4. Ink thickness variations may also be computed, when the nominalsurface coverages of the target halftone area segment are unknown, bymeasuring under reference settings, for a halftone area segment,reference sensor values, by deriving a corresponding set of referenceeffective surface coverages and by computing for the same halftone areasegment in the following printed sheets, the ink thickness variations byminimizing a distance metric between the sensor values predictedaccording to the reference effective surface coverages and the currentlymeasured sensor values.

The disclosed simple and non-expensive solid device sensing system makeink thickness variation prediction and therefore the regulation of printactuation variables applicable to many different kinds of printingdevices, from expensive large format printing devices to small and cheapprinting devices.

REFERENCES CITED

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1. A method for computing ink thickness variations for the control ofprinting devices, the method being based on an ink thickness variationand sensor response enhanced spectral prediction model, said methodcomprising calibration steps and, during print operation, online inkthickness variation computation steps, where the calibration stepscomprise the calculation of ink transmittances, and where the inkthickness variation computation steps comprise fitting of ink thicknessvariations by minimizing a distance metric between predictedmulti-channel sensor responses and acquired multi-channel sensorresponses, said predicted multi-channel sensor responses being computedaccording to the ink thickness variation and sensor response enhancedspectral prediction model, and said. acquired multi-channel sensorresponses being generated by light reflected on a print sheet.
 2. Themethod of claim 1, where the print sheet is moving and the multi-channelsensor devices, due to their high-speed acquisition capabilities,provide responses according to the reflectance of small area segmentswithin the print sheet, and where the calibration steps also comprise,in order to account for ink spreading, fitting of effective surfacecoverage curves mapping nominal to effective surface coverages of singleink halftones in different superposition conditions.
 3. The method ofclaim 1, comprising also during said print operation online calibrationsteps, said online calibration steps comprising a step of fittingeffective surface coverage curves mapping nominal to effective surfacecoverages of single ink halftones in different superposition conditionsby acquisition of sensor responses from polychromatic halftones.
 4. Themethod of claim 1, where the thickness variation and sensor responseenhanced spectral prediction model comprises as solid coloranttransmittance of at least two superposed solid inks the transmittance ofeach of the superposed inks raised to the power of a product ofvariables, one variable being the superposition condition dependent inkthickness and the other variable being the ink thickness variationfactor.
 5. The method of claim 1, where the inks are the cyan, magenta,yellow, and black inks and where the thickness variation and sensorresponse enhanced spectral prediction model operates simultaneously inthe visible and near infra-red wavelength range domain.
 6. The method ofclaim 1, where the ink thickness variation computation steps alsocomprise the step of online recording of reference thickness variationsand where the computed ink thickness variations are ink thicknessvariations normalized in respect to the reference ink thicknessvariations.
 7. The method of claim 1, where, in addition to thecalibration and recalibration steps, the step of acquiring during printoperation reference sensor responses from a reference print underreference settings and of deducing corresponding reference effectivesurface coverages is performed, where the sensor responses are predictedwith the deduced reference effective surface coverages, and where thecomputed ink thickness variations represent ink thickness variations inrespect to the reference print.
 8. The method of claim 1, where saidmulti-channel sensor devices are based on single photon avalanche diodes(SPADs) which capture during print operation light reflected by saidsmall area segments within the print page.
 9. The method of claim 8,where light emitting diodes (LEDs) emit light that is directed towardsthe print sheet, where part of said light penetrates the print sheet, isreflected by the sheet's substrate and captured by said SPAD sensordevices.
 10. An ink thickness variation computing system for the controlof printers, respectively printing presses operable for the onlinecomputation of ink thickness variations during print operation, said inkthickness variation computing system comprising multi-channel sensordevices, a processing module, and a computing system, where themulti-channel sensor devices respond at different spectral sensibilityranges within the visible and near infra-red wavelength range, where themulti-channel sensor devices, due to their high-speed acquisitioncapabilities, provide responses according to the reflectance of smallarea segments within a print sheet, where the processing module receivesthe responses from said multi-channel sensor devices and forwards themto the computing system, which according to an ink thickness variationand sensor response enhanced spectral prediction model deduces said inkthickness variations.
 11. The ink thickness variation computing systemof claim 10, where said multi-channel sensor devices are based on singlephoton avalanche diodes (SPADs) which capture light reflected by saidsmall area segments within the print sheet.
 12. The ink thicknessvariation computing system of claim 11, where single photon avalanchediodes photon count acquisition times range between 200 nanoseconds and10 milliseconds.
 13. The ink thickness variation computing system ofclaim 11, where the processing module comprises a multiplexer, a fastlogic, a pulse counter and a microcontroller, where the multiplexer isoperable for selecting the SPAD whose pulses are counted, where thepulse counter is operable for counting the pulses received from theSPADs and where the microcontroller is operable for storing theresulting pulse count and for transmitting it to the computing system.14. The ink thickness variation computing system of claim 11, wherelight emitting diodes (LEDs) emit light that is directed towards theprint sheet, where part of said light penetrates the print sheet, isreflected by the sheet's substrate and captured by said SPAD sensordevices.
 15. The ink thickness variation computing system of claim 11,where white light is filtered by filters having different spectralsensibilities within the visible and near infra-red wavelength range anddirected towards the print sheet, where part of said filtered lightpenetrates the print sheet, is reflected by the print sheet's substrateand captured by said SPAD sensor devices.
 16. The ink thicknessvariation computing system of claim 11, where white light illuminates anarea segment of said print sheet, is reflected by said area segment, isfiltered by filters having different spectral sensibilities within thevisible and near infra-red wavelength range and is captured by said SPADsensor devices.
 17. The ink thickness variation computing system ofclaim 11, where one input and one output polarizing filters discard partof said light that is specularly reflected at the surface of said movingprint sheet.
 18. The ink thickness variation computing system of claim10 forming together with an additional print actuation parameter drivingmodule an online ink regulation system operable for controllingaccording to the deduced ink thickness variations the amount of inkdeposited onto a substrate.
 19. The ink thickness variation computingsystem of claim 18, where controlling the amount of ink deposited onto asubstrate is performed in case of a printed press by ink feed, in caseof an ink jet printer by a function selected from the set of dropletejection control and droplet count, in case of an electrophotographicprinter by a function selected from the set of toner transfer and fusingand in case of a thermal transfer, respectively dye sublimation printer,by controlling head element temperature profiles.
 20. The ink thicknessvariation computing system of claim 10, where the inks are the cyan,magenta, yellow, and black inks and where said thickness variation andsensor response enhanced spectral prediction model operates in thevisible and near infra-red wavelength range.
 21. The ink thicknessvariation computing system of claim 10, where said computing system alsoperforms an online refined calibration of said thickness variation andsensor response enhanced spectral prediction model by deducing paperreflectances of said print sheets and by fitting according to themulti-channel sensor responses effective surface coverage curves mappingnominal to effective surface coverages of single ink halftones indifferent superposition conditions.
 22. The ink thickness variationcomputing system of claim 10, where said computing system also recordsreference thickness variations and where the computed ink thicknessvariations are ink thickness variations normalized in respect to thereference ink thickness variations.
 23. The ink thickness variationcomputing system of claim 10, where said computing system also recordsreference sensor responses from a reference print under referencesettings, deduces corresponding reference effective surface coverages,and predicts sensor responses with the deduced reference effectivesurface coverages and where the computed ink thickness variationsrepresent ink thickness variations in respect to the reference print.